test

Jan 2010
17
1
\(\displaystyle
\left(\begin{array}{cc}n\\n_{1},n_{2}, ..., n_{k}\end{array}\right) = \frac{n!}{n_{1}!n_{2}!...n_{k}!}
\)

\(\displaystyle
P(X=k) = \frac{1}{n}
\)

\(\displaystyle
E(X) = \frac{n+1}{2}
\)
\(\displaystyle
V(X) = \frac{n^{2}-1}{12}
\)

\(\displaystyle
= \frac{P(A_{i}) \times P(E \mid A_{i})}{P(A_{1}) \times P(E \mid A_{1}) + P(A_{2}) \times P(E \mid A_{2}) + ... + P(A_{n}) \times P(E \mid A_{n})}
\)
 
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MHF Hall of Honor
Mar 2010
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Chicago
\(\displaystyle
\left(\begin{array}{cc}n\\n_{1},n_{2}, ..., n_{k}\end{array}\right) = \frac{n!}{n_{1}!n_{2}!...n_{k}!}
\)

\(\displaystyle
P(X=k) = \frac{1}{n}
\)

\(\displaystyle
E(X) = \frac{n+1}{2}
\)
\(\displaystyle
V(X) = \frac{n^{2}-1}{12}
\)

\(\displaystyle
= \frac{P(A_{i}) \times P(E \mid A_{i})}{P(A_{1}) \times P(E \mid A_{1}) + P(A_{2}) \times P(E \mid A_{2}) + ... + P(A_{n}) \times P(E \mid A_{n})}
\)
Depending on your preferences you might also like to use \cdot so that \(\displaystyle P(A_{i}) \times P(E \mid A_{i})\) becomes \(\displaystyle P(A_{i}) \cdot P(E \mid A_{i})\).